The electromechanical time constant of a servo motor includes both electrical and mechanical time constants. Distinguishing between the electrical and mechanical time constants during testing is difficult, and since the electrical time constant is typically much smaller than the mechanical time constant, they are generally not separated in engineering applications and testing.
The testing principle of the electromechanical time constant of a servo motor is mainly based on the definition of electromechanical time constant and the dynamic theory of motors. The national standard recommends several testing methods, including the starting current method, the control current method, the tachometer method, and the drag method. The following article will introduce the principles and operation of these testing methods.
I. Definition of Servo Motor Time Constant
The GB/T2900 terminology for controlled motors defines electromechanical time constant, mechanical time constant, and electrical time constant as follows:
01 Electromechanical Time Constant Tme
The electromechanical time constant is the time required for a servo motor to increase its speed from zero to 63.2 % of its no-load speed under no-load and rated excitation conditions, when a step-voltage rated control voltage is applied.
02 Mechanical Time Constant Tm
The specific calculation methods for DC servo motors and AC servo motors can be expressed using parameters such as motor terminal resistance R, moment of inertia Jm, back EMF coefficient Ke, and torque constant KT.
03 Electrical Time Constant Te
It can be represented by the motor terminal resistance R and inductance L:
II. Servo Motor Electromechanical Time Constant Test 01 Starting Current Method
According to the dynamic theory of DC motors, the following formula can be obtained:
In the formula:
ua — Armature voltage, measured in volts (V);
Ia — Armature current, measured in amperes (A);
Ra – armature resistance, measured in ohms (Ω).
tM — Electromechanical time constant, in seconds.
The time it takes for the current to decrease from its maximum value to 63.2 % during no-load starting of the motor is the electromechanical time constant tM. During testing, the motor stator is fixed, and no load is applied to the motor shaft. Rated excitation is applied to the excitation winding of the energized motor, and a rated step voltage is applied to the armature winding. The complete waveform of the starting current during the application of the step voltage is recorded using waveform acquisition equipment. The time constant of the motor is then obtained through waveform data processing.
02 Control Current Method
Similar to the starting current method, it can be concluded that...
In the formula:
ua — Point voltage, unit is volt (V);
Ia — Armature current, measured in amperes (A);
Ra – armature resistance, measured in ohms (Ω).
tM — Electromechanical time constant, in seconds (s);
The time taken for the current to decrease from its maximum value to 63.2 % during no-load braking of the motor is the electromechanical time constant tM. During testing, the motor stator is fixed, and no load is applied to the motor shaft. Rated excitation is applied to the excitation winding of the energized motor, and rated voltage is applied to the armature winding. After the motor speed stabilizes, the armature winding voltage is disconnected, and the armature winding is immediately disconnected from the circuit. The complete waveform of the control current during the process from the disconnection of the armature winding to the motor stopping is recorded using waveform acquisition equipment. Then, the time constant of the motor is obtained through waveform data processing.
03 Tachometer Method
The relationship between the output voltage and speed of the tachogenerator under no-load conditions is as follows:
In the formula:
ua — Generator output voltage, in volts (V);
Kb — Motor constant, measured in volt-seconds per radian ( V.s /rad);
Figure 1: Wiring diagram for tachometer method
During testing, a low-inertia tachogenerator and the motor under test are rigidly connected and fixed coaxially, with wiring as shown in Figure 1 above. A rated step voltage UN is applied to the motor, causing the motor to drive the tachogenerator to rotate together until the speed stabilizes. The voltage waveform of the tachogenerator is recorded on a waveform acquisition device, and the time taken for the voltage to rise from zero to 63.2 % of its steady-state value is calculated from the waveform diagram; this is the electromechanical time constant.
N – Generator speed, in revolutions per minute (r/min).
When the tachogenerator is coaxially connected to the motor under test, and the motor is started with a step voltage, it drives the tachogenerator to rotate and generate an output voltage. As can be seen from the above formula, the output voltage of the tachogenerator is proportional to the speed of the motor. As long as the rising waveform of the output voltage of the tachogenerator is measured, the electromechanical time constant of the motor can be calculated.
04 Towing Method
In the formula:
ub — Generator armature voltage, measured in volts (V);
kb — motor constant, measured in volt-seconds per radian (V · s/rad);
ua — Armature voltage of the electric motor, measured in volts (V);
ka — Motor constant, in volts; Motor constant, in volt-seconds per radian (V · s/rad).
tM — Combined electromechanical time constant, in seconds (s).
The rise curve of the generator armature voltage ub is linearly related to the unit's rotational angular velocity. The time taken for the voltage to rise from zero to 63.2 % of its steady-state value can be obtained from the ub curve. This time is the combined time constant tM.
Figure 2: Wiring diagram for the topper method
The motor under test is rigidly connected coaxially to another motor with a known electromechanical time constant. One motor operates as a motor, and the other as a tachogenerator, connected as shown in Figure 2 above. A rated step voltage UN is applied to the motor, and the output voltage waveform of the tachogenerator is measured. The method for determining the time constant is the same as the tachometer method, except that the obtained time constant is the combined electromechanical time constant. For two motors with identical models and specifications, the electromechanical time constant calculated from the waveform is divided by 2 to obtain the electromechanical time constant of the motor under test. If the two motors have different models and specifications, the electromechanical time constant of the tachogenerator should be known beforehand. Then, the electromechanical time constant of the tachogenerator is subtracted from the electromechanical time constant tM calculated from the waveform to obtain the electromechanical time constant of the motor under test.
